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### Trisecting an Angle Using the Conchoid of Nicomedes

```Date: 08/16/2002 at 20:30:39
From: J. A. Greene
Subject: Trisecting an angle and using a Nichomedian choncoid

I attempted to trisect an angle using the Nichodemian Choncoid (which
I constructed using a compass and straightedge), and I showed it to my
dad, who said that it was 100% impossible to do so, and I showed it to
my mom, who said that I might actually have trisected the angle.  I
want to know if it possible that I could have trisected it using the
conchoid.

JA Greene
```

```
Date: 08/16/2002 at 23:13:37
From: Doctor Peterson
Subject: Re: Trisecting an angle and using a Nichomedian choncoid

Hi, J. A.

Of course it is possible! The Greeks invented this curve for the
purpose of trisecting angles; it's nothing new. The problem is that it
doesn't follow the rules for a compass and straightedge construction,
which must use NOTHING else. That is what is impossible, not
trisection using other tools. You didn't really construct the curve
with compass and straightedge alone, since it is not composed only of
lines and circles; you must have constructed some points and then
drawn a curve through them somehow.

See the Dr. Math FAQ:

Impossible constructions
http://mathforum.org/dr.math/faq/faq.impossible.construct.html

St. Andrews University::

Trisecting an angle
<http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/
Trisecting_an_angle.html>

And see this on the conchoid:

Conchoid of Nicomedes - Xah Lee
<http://www.xahlee.org/SpecialPlaneCurves_dir/
ConchoidOfNicomedes_dir/conchoidOfNicomedes.html>

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Constructions

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